We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement variational manifolds and target Hamiltonians with classical ground states. Despite the presence of highly entangled intermediate states along the exact quantum annealing path, the variational evolution converges to the target ground state. We demonstrate this approach with several examples that align with our theoretical analysis.